
Principles of Macroeconomics (MindTap Course List)
7th Edition
ISBN: 9781285165912
Author: N. Gregory Mankiw
Publisher: Cengage Learning
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Chapter 9.2, Problem 2QQ
To determine
The impact of international trade on total surplus.
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Choose all correct answers regarding the estimated multiple linear regression model:
ŷ = ߸ + ß‚× + ². Assume that ẞ, and ẞ are both non-zero.
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(a) The estimated regression function is represented by a plane in three-dimensional space.
(b) It gives the value of y, for each value of x, such that half the values of y are above the
function and half are below.
(c) The predicted value of y with x₁ = 1 and x2 = 1 is ẞ + Â₁ + Â₂
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(d) If you use robust option in Stata, then ẞ, becomes either smaller or larger in magnitude.
Determine whether the following statement is true or false.
In a simple linear regression,
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if E[ulx] = 0, the estimate of ẞ₁ is statistically significant.
Explain your answer in two sentences or fewer.
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0
Choose all the correct answers based on the figure below
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T
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2
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(a) The coefficient of x is not statistically significant
(b) The explained sum of squares is less than the total sum of squares
(c) The independent variable is a dummy variable
(d) The assumption of homoskedasticity is not likely to hold
Chapter 9 Solutions
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- Determine whether the following is true or false: In a multiple linear regression, y = ẞ₁ + ẞ₁x, + ẞ₂×₂ + u, 0 if corr(x,, x) = 1, then ẞ, cannot be estimated, because the numerator in the formula for ß, is zero. Explain your answer in two sentences or fewer.arrow_forwardChoose all correct answers regarding assumptions for B₁ in a simple linear regression. (a) If there is no variation in X, we cannot identify the estimate of ẞ₁, so E[ẞ₁] = ẞ, does not hold. (b) It measures the y-intercept of the estimated regression line. (c) As the sample size increases, ẞ₁ is more likely to be closer to ẞ, assuming E[ß₁] = ß₁. (d) If the sample covariance between x and y is positive, then B₁ > 0.arrow_forwardChoose all correct answers regarding the multiple linear regression model: y = Bo+ B₁x₁ + B2X2 + + BkXk + U. (a) If you add a relevant variable XK+1, but corr(XK, Xk+1) is high, then you must not include xk+1 in the regression equation. (b) Adding a variable XK+₁ may lower the R² value. (c) Adding all the variables in the dataset does not imply that E[u | X1, X2, ... Xk] = 0. (d) We can estimate the value of ẞ₁ by minimizing Σ(û¡)².arrow_forward
- Refer to the Stata output from an analysis of data on Store sales. The data include nominal store-level sales (measured in for the month of June 1996 from 844 stores of a national retail chain. The other variables are: A categorical string variable loctype which indicates the type of store location and takes one of three values: "mall" = 1 if the store is located in a shopping mall (indoor or outdoor) "street" = 1 if the store is located on a street "strip" = 1 if the store is located on a strip or highway ⚫ medhhinc = the median household income of the city where the store is located, measured in $1,000 • empl = the total number of employees working in the store in June 1996 . sqft = the store's size, measured in 1,000 square feet A manager wants to know how average monthly sales varies with the characteristics of a store and its location and uses Stata to perform the regression analysis shown. gen sqftXmedhhinc =sqft*medhhinc . reg sales mall street medhhinc empl sqft sqftXmedhhinc,…arrow_forwardWe would like to examine whether there is a differential effect of study hours on test scores between students whose first language is English and those whose first language is not English by adding an interaction term. gen hoursEng = study_hours *English . reg test_score study_hours English hoursEng Source SS df MS Number of obs 876 Model Residual 136565.839 18952.9115 3 45521.9464 872 21.7349902 F(3, 872) Prob F 2094.41 0.0000 R-squared 0.8781 Total 155518.751 875 177.735715 Adj R-squared = Root MSE 0.8777 = 4.6621 test_score Coef. Std. Err. t P>|t| [95% Conf. Interval] study_hours English hoursEng 1.82049 .0369748 49.24 0.000 8.318905 .8108202 10.26 0.000 .101876 cons 43.52037 .0516819 .5767457 1.97 75.46 0.049 0.000 1.74792 6.727517 .0004404 42.3884 1.89306 9.910292 .2033115 44.65234 (a): What is the predicted test score for an individual who studied two hours and whose first language is not English? (Round to two decimal places) (b): Choose all correct answers (a) The differential…arrow_forwardDetermine whether the following statement is true or false. Suppose you reject the null hypothesis: Ho: ẞ₁ = ẞ₂ = 0. Then, both ẞ₁ = 0 and ẞ2 ± 0. Explain your answer in two sentences or fewer.arrow_forward
- Choose one correct answer: The ---A----- dataset includes 100,000 students from 512 schools observed over 12 months. To control differences between schools and months, we should add a total of What are A and B? (a) A: Time series, B: 524 (b) A: Time series, B: 522 (c) A: Panel, B: 524 (d) A: Panel, B: 522 dummies.arrow_forwardRefer to the Stata output from an analysis of data on Store sales. The data include nominal store-level sales (measured in for the month of June 1996 from 844 stores of a national retail chain. The other variables are: A categorical string variable loctype which indicates the type of store location and takes one of three values: "mall" = 1 if the store is located in a shopping mall (indoor or outdoor) "street" = 1 if the store is located on a street "strip" = 1 if the store is located on a strip or highway ⚫ medhhinc = the median household income of the city where the store is located, measured in $1,000 • empl = the total number of employees working in the store in June 1996 . sqft = the store's size, measured in 1,000 square feet A manager wants to know how average monthly sales varies with the characteristics of a store and its location and uses Stata to perform the regression analysis shown. gen sqftXmedhhinc =sqft*medhhinc . reg sales mall street medhhinc empl sqft sqftXmedhhinc,…arrow_forwardEssay question. In this regression analysis, you are interested in the effect of age on the amount of gasoline used by a car, measured in gallons. Suppose you analyze your dataset and find the following results. Based on the Stata output, how can you improve the analysis? State 3 issues in the figure and table, and possible solution for each problem you can apply based on what you have learned in class. gasoline_use 40 20 100 .reg gasoline_use age Source SS df MS Model Residual 28.1117271 9969.5248 1 28.1117271 23 433.4576 Number of obs F(1, 23) Prob > F R-squared 25 0.06 0.8012 0.0028 a Total 9997.63653 24 416.568189 Adj R-squared Root MSE -0.0405 20.82 gasoline_use Coef. Std. Err. t P>|t| [95% Conf. Interval] age cons -.0688645 .2704114 62.37748 13.86839 -0.25 0.801 4.50 0.000 -.6282532 .4905242 33.68853 91.06643 20 40 60 80 agearrow_forward
- The regression below examines the relationship between CEO salary (measured in thousands of dollars) and grad, whether the CEO has a graduate degree (an indicator variable), their years of tenure as CEO, and the profits of the company (in millions of dollars). Source SS df MS Number of obs 177 F(3, 173) 12.56 Model Residual 10867017.6 3 3622339.19 Prob > F 0.0000 173 288433.221 R-squared 0.1788 Adj R-squared 0.1646 Total 176 345261.163 Root MSE 537.06 salary Coef. Std. Err. t P>|t| [95% Conf. Interval] grad tenure -31.47414 81.70146 -0.39 0.701 129.7859 12.22944 2.15 0.033 .9951956 23.46368 profits .5807776 .1005807 5.77 0.000 .3822544 .7793009 cons 664.5934 79.02213 8.41 0.000 508.6218 820.565 (a): Perform the hypothesis that Ho: ẞprofits 0.7. What is the t statistic? (Round to one decimal place) (b): Let tcritical 2 given a = 0.05. Is profits statistically different from 0.7 at 5% significance level?arrow_forwardFILL IN THE BLANK, FILL IN $(A)arrow_forwardreg bwght cigs Source SS df MS Number of obs 1,200 F(1, 1198) 27.19 Model 10309.4151 Residual 454313.622 1,198 1 10309.4151 379.226729 Prob F 0.0000 R-squared 0.0222 Adj R-squared = 0.0214 Total 464623.037 1,199 387.508788 Root MSE = 19.474 bwght Coef. Std. Err. t P>|t| [95% Conf. Interval] cigs _ cons -.4847414 119.6458 .0929699 .5961203 -5.21 200.71 0.000 0.000 -.6671434 118.4762 -.3023394 120.8153 reg bwght cigs faminc Source SS df MS Model Residual 13744.9489 450878.088 2 6872.47446 1,197 376.673423 Number of obs F(2, 1197) Prob > F = 1,200 18.25 0.0000 R-squared == 0.0296 Total 464623.037 1,199 387.508788 Adj R-squared = Root MSE = 0.0280 19.408 bwght Coef. Std. Err. t P>|t| [95% Conf. Interval] cigs -.4344055 .0941436 faminc .0305302 _ cons 116.8568 1.098078 -4.61 3.02 106.42 0.000 0.003 0.000 -.6191102 -.2497007 .0323041 114.7025 .1521013 119.0112 reg taminc cigs Source SS df MS Model Residual 13076.2081 404116.459 1 13076.2081 1,198 337.325925 Number of obs = F(1, 1198) Prob F…arrow_forward
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